Argentina's military command plunged into a heavy new round of fighting in the South Atlantic today while facing the loss of hundreds of lives on the sunken Argentine cruiser General Belgrano. By late today, the military command reported that 680 of the ship's 1,042 crew had been saved and that rescue efforts were continuing.

The Argentine military command officially reported early tonight that forces on the Falkland Islands had shot down two British Sea Harrier jets taking part in a bombing raid on the airfield at Darwin this afternoon. The communique said there were no Argentine losses.

Naval officials who asked not to be named said that the British destroyer Sheffield had been sunk during an Argentine air attack. They said the attack was carried out by a squadron of six Argentine Super Etendard fighter-bombers firing Exocet missiles. The French-made jets are designed to be launched from an aircraft carrier. The missiles also are French-made.

However, the Argentine joint chiefs of staff did not officially confirm the sinking of the destroyer. In a communique the military command said that an Argentine air attack had been carried out on the British fleet at 9:50 a.m. EDT today 60 miles southeast of the Falklands "with results that are still not known."

The communique said two British air attacks on the Falklands occurred today; one, at Port Stanley airport, at 4:30 a.m. EDT and one, at Port Darwin airstrip, at noon. It was in the second attack that the two British Sea Harriers were shot down, according to the statement.

As the new air battles broke out around the Falklands, government sources said the military command, and in particular the Argentine Navy, was determined to exact revenge for the torpedoing of the cruiser Belgrano.

With much of Argentina fixed on what threatened to become the greatest military loss of life in modern Argentine history, government officials said there was little optimism about a diplomatic accord with Britain, even for a cease-fire in the South Atlantic.

Government sources here said tonight that Argentina would probably ask the Soviet Union to veto any move for a cease-fire plan in a special session of the U.N. Security Council.

Amid a rising tide of anti-American sentiment, Foreign Ministry sources said Foreign Minister Nicanor Costa Mendez saw little prospect of any further mediation role involving the United States.

The U.S. Embassy issued a sharp denial of press reports here that the United States provided information on the Belgrano to Britain. Shortly afterward, the embassy announced that "nonessential personnel" and members of some families of embassy officials had been asked to leave Argentina temporarily due to "the tragic conflict the South Atlantic and the unsettled conditions it has created."

Embassy officials said about 7,000 Americans were now living in Argentina.

The Argentine naval officials said a tug, first identified as a patrol boat, carrying a crew of 50 to 80 radioed that it was limping into port after being attacked yesterday by two British helicopters. The officials still could not give details on the pilot whom they said the American-built, 800-ton tug sought to rescue when attacked.

Britain has reported that its helicopters sank one patrol boat and damaged another yesterday after another copter was fired upon. The differences in the versions could not be resolved here.

The officials said the tug, the Sobral, radioed that it was damaged but it was not known if any of the crew had been killed or injured.

The state-owned Telam news agency, meanwhile, said 11 civilians were killed and 17 wounded in British helicopter attacks Saturday on Darwin in the Falklands. This report could not be confirmed elsewhere.

Both government and civilian leaders here appeared shocked by the fate of the Belgrano, an aging World War II-era cruiser that disappeared from Argentine radar screens shortly after noon yesterday in the stormy, frigid waters off the eastern tip of South America, according to reports here.

Military officials offered no estimate by late today of how many of those still missing might be saved. The Foreign Ministry put the crew total at 1,042, hence a 362 figure for the missing. However, some unofficial reports said fewer than 1,042 actually were aboard. Authorities released a phone number at the naval base of Puerto Belgrano south of Buenos Aires for families to call for information.

A flotilla of boats and planes worked through last night and today to rescue the ship's crew, which was forced into lifeboats some 17 hours after the ship was torpedoed by a British submarine Sunday night, according to military officials. The daily paper Clarin reported that the cruiser sank after it was struck by a storm early Monday.

As a series of terse communiques slowly raised the number of crew reported rescued during today, hospitals were cleared in southern cities and outside Buenos Aires to receive the wounded. Planes carried the injured--wearing red, yellow or white bracelets to indicate the seriousness of their condition.

Early this evening, the governor of Tierra del Fuego, nearest the sinking, announced that 400 of the ship's survivors were in good condition and were expected to arrive in the port of Ushuaia tonight.

Reports reaching Buenos Aires said one Argentine vessel had been converted into a hospital ship near the scene, and a ship from the rival Chilean Navy had sailed into the Atlantic to join the search.

Navy commander-in-chief and junta member Jorge Anaya was reported to say this morning that "this loss . . . will strengthen the decision to continue the fight until the complete achievement of the proposed objective, defense of our sovereignty" over the Falklands.

The statement, made in a message transmitted to Argentine naval forces, signaled an apparent determination to take on the British both militarily and diplomatically rather than back down in the increasing crisis.

Some Argentine sources here blamed this tough position on the relentlessness of the British attack. "The military would be inclined to reflect on their situation after losing the Belgrano," said one source close to the military here. "But there has been no time for that. They have turned immediately to planning for the next British attack."

Government sources said Foreign Minister Costa Mendez told Foreign Ministry officials in a meeting today that no clear route to a diplomatic solution of the crisis was open at this time.

Argentine officials said that a plan by U.N. Secretary General Javier Perez de Cuellar for an end to the fighting was "under study," but that the plan's chances seemed small in light of indications by British officials that U.N. mediation was not acceptable.

Government sources also said that Argentina saw little prospect for positive action emerging from the meeting the U.N. Security Council requested by Ireland. Costa Mendez met today with the Irish ambassador for a short time, but a Foreign Ministry official said the most likely result of the Security Council meeting was "a cross veto" of a truce call--that is, vetoes both by Britain and the Soviet Union, acting on Argentina's behalf.

Some Argentine officials have said they expected the Soviet Union to veto Security Council resolution introduced by Britain shortly after Argentina's invasion of the Falklands on April 2. It called for an Argentine withdrawal. The Soviet Union, however, abstained on the measure. Since then, however, Soviet statements have promised strong diplomatic support for Argentina against Britain.

Argentine and diplomatic officials here said they saw little immediate prospect for a successful attempt by the United States to introduce a diplomatic plan acceptable to both Argentina and Britain. Argentine officials indicated that it was believed by at least some sectors of the Argentine government that what they described as the last U.S. proposal to Argentina--transmitted through the Peruvian government--had been made only in an attempt to place more pressure on Argentina by forcing it to reject a plan it had already said was unacceptable.

Argentina said in a communique issued on Sunday that the plan differed little from the last U.S. plan offered to Argentina last week.

With anti-U.S. sentiment appearing to rise quickly in civilian sectors here, the morning paper Nacion accused the United States of trying to "draw in the international forum the image of a government deaf to whatever negotiated offer."